The index with respect to a rigid subcategory of a triangulated category

P Jørgensen, A Shah - International Mathematics Research …, 2024 - academic.oup.com
Palu defined the index with respect to a cluster tilting object in a suitable triangulated
category, in order to better understand the Caldero–Chapoton map that exhibits the …

On the lattices of exact and weakly exact structures

RL Baillargeon, T Brüstle, M Gorsky, S Hassoun - Journal of Algebra, 2022 - Elsevier
We initiate in this article the study of weakly exact structures, a generalisation of Quillen
exact structures. We introduce weak counterparts of one-sided exact structures and show …

[HTML][HTML] Grothendieck groups of d-exangulated categories and a modified Caldero-Chapoton map

P Jørgensen, A Shah - Journal of Pure and Applied Algebra, 2024 - Elsevier
A strong connection between cluster algebras and representation theory was established by
the cluster category. Cluster characters, like the original Caldero-Chapoton map, are maps …